Triangle Types and Midpoint Calculations

This video tutorial covers the basics of analytic geometry, focusing on finding the midpoint and length of line segments. It explains the midpoint formula and how to use the Pythagorean theorem to calculate the length of a line segment. The tutorial includes several examples, ranging from simple to complex, involving fractions and unknowns. It concludes with a section on classifying triangles by side length and verifying right angles using the Pythagorean theorem.

What is the first step in finding the midpoint of a line segment?

• Add the x-coordinates of the endpoints and divide by two.

• Multiply the x-coordinates of the endpoints.

• Subtract the y-coordinates of the endpoints.

• Divide the y-coordinates of the endpoints by two.

Which theorem is used to derive the formula for the length of a line segment?

• Pythagorean theorem

• Remainder theorem

• Binomial theorem

• Fundamental theorem of calculus

In Example 1, what is the x-coordinate of the midpoint of line segment CD?

• 0

• 1/2

• -1

• -1/2

In Example 1, what is the approximate length of line segment CD?

• 12.0 units

• 9.5 units

• 10.3 units

• 11.2 units

In Example 2, what is the y-coordinate of the midpoint of line segment AB?

• 4

• 5

• 3

• 2

In Example 2, what is the exact length of line segment AB?

• √17

• √34

• √106

• √145

In Example 3, what is the x-coordinate of the midpoint of line segment EF?

• 27/16

• 3/4

• 7/16

• 5/8

In Example 3, what is the approximate length of line segment EF?

• 7.89 units

• 6.34 units

• 4.67 units

• 5.12 units

In Example 4, what are the coordinates of point B if point A is (5, 7) and the midpoint is (4, 8)?

• (3, 9)

• (4, 9)

• (5, 8)

• (6, 7)

In Example 5, what type of triangle is DEF based on side lengths?

• Equilateral

• Right

• Scalene

• Isosceles